This invention is directed to a system for estimating the launch point of a missile from Doppler data. The launch point of the missile can be estimated from Doppler by standard differential correction techniques. However, these techniques do not give an accurate estimate of the launch point because of a lack of sensitivity of the techniques to cross range error. More specifically, the launch point error can be decomposed into a downrange error which is the error parallel to the azimuth of the missile velocity and a cross range error which is error perpendicular to the missile velocity. With Doppler measurements alone, standard differential correction techniques result in small downrange error, but achieve very little reduction in the cross range error relative to the initial estimate of the launch position. As a result, the accuracy of the launch point is adversely constrained by the cross range error in the initial estimate of the launch point.
In earth centered fixed coordinates (ECF), the launch point is estimated by its latitude and longitude and is equivalent to a two-dimensional problem. In accordance with the invention, the cross range error in the estimation is reduced by decoupling this two-dimensional problem into two one-dimensional problems. This decoupling is carried out by changing the coordinate system from ECF to rotated earth fixed coordinates (REF). The ECF coordinate system is a Cartesian coordinate system having its center of origin at the center of the earth and having a Z-axis extending between the poles of the earth. An X-axis extends from the origin to the intersection of the equator and the prime meridian and a Y-axis extends perpendicular to the X-axis in the plane of the equator. To convert this system in accordance with the invention to REF, which is also a Cartesian coordinate system having its origin at the earth""s center, the X-axis is rotated to extend from the origin or earth""s center to the estimated launch point and the Z-axis is rotated to be parallel to the azimuth of the missile velocity. The Y-axis will then be parallel to the cross range movement of the missile. In this REF coordinate system, the measurements are angular measurements like latitude and longitude. Position estimates along the Z-axis, called downrange estimates, are equivalent to latitude measurements and position estimates along on the Y-axis, called cross range estimates, are equivalent to longitude estimates. In accordance with the invention, the cross range estimate is held fixed and the error in the downrange component of the launch point estimate is reduced to a minimum using differential correction techniques. The solving of this problem is essentially a one-dimensional problem and decoupling of the problem from the cross range component of the launch point estimate is possible because the Doppler measurements predicted from the estimated missile trajectory have very little sensitivity to the cross range component of the launch point error. Thus, the process provides an accurate estimate of the downrange component of the launch point, but the cross range component still needs to be determined. In order to reduce the cross range error in the launch point estimate, a coordinate system must be selected, the axes of which are not parallel to the azimuth of the missile velocity. In the second phase of the process, to obtain an accurate estimate of the cross range component of the launch point, the coordinates are rotated to a second REF coordinate system in which the X-axis is again positioned to extend from the earth""s center to the updated estimated launch point and the Z-axis is rotated 45 degrees with respect to the missile velocity azimuth. In this coordinate system changes in the Z component of the launch point position correspond to changes in both the downrange and cross range components of the launch point. Similarly, changes in the Y component in this coordinate system corresponds to changes in both the downrange and the cross range components of the launch point. In the second stage of the algorithm, the current estimate of either the Y component or the Z component, corresponding to longitude or latitude in REF coordinates, is held constant and the launch point is searched for within a narrow band which is rotated 45 degrees with respect to the initial direction of missile motion again using differential correction techniques. This second stage of computation is again essentially a one-dimensional problem. The second stage can be iterated to the extent necessary to achieve a desired accuracy by searching for the launch point along axes which are rotated at a variety of angles with respect to the missile azimuth.
In order to carry out the above-described method, the knowledge of the missile""s velocity azimuth is required. The Doppler measurements provide accurate data from which the missile velocity can be estimated using a Kalman filter. The azimuth of the missile velocity is computed from the velocity vector prior to the first stage cutoff.